Greediness does not work in general. What if your categories have sizes 15, 15, 10, 10, 15, 15? Your solution comes out with a suboptimal answer.

That's what backtracking's for. :-)

Actually, that brings up an interesting question: Ovid, are there any bounds on how optimal the answer has to be? Exactly optimal (sucky if this problem turns out to be NP-Hard)? Within a constant factor of optimal (like, max length no more than 1.5x larger than optimal)?

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The hell with paco, vote for Erudil!
:wq